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A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source

Journal of Agricultural, Biological and Environmental Statistics volume 27, pages 46–62 (2022)Cite this article

Abstract

Point sources in spatially referenced data can impact outcomes in surrounding locations (e.g., a factory that emits air pollution). Previous statistical methods have sought to describe the non-stationary correlation induced by the presence of a point source, with fewer attempting to quantify its overall impact. We introduce directionally varying change points (DVCP), a model that aims to estimate the magnitude of the impact of a point source as well as its range of influence across the spatial domain. DVCP allows for a unique change point parameter, describing the range of influence of a point source, at every angle extending from the source and uses a Gaussian process with directionally defined correlation function to facilitate estimation of the parameters. The Gaussian predictive process approximation is used for fitting the model to large datasets. Through simulation, we show that DVCP can easily accommodate a wide range of shapes defining the range of influence. We apply DVCP to better understand spatial patterns of ambient PM\(_{2.5}\) concentrations and issues related to environmental inequity in California and Colorado. The method is available in the R package DVCP.

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References

  • Ash M, Fetter TR (2004) Who lives on the wrong side of the environmental tracks? Evidence from the EPA’s risk-screening environmental indicators model. Soc Sci Q 85(2):441–462

  • Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J R Stat Soc Ser B (Stat Methodol) 70(4):825–848

    Article  MathSciNet  MATH  Google Scholar 

  • Bell ML, Ebisu K (2012) Environmental inequality in exposures to airborne particulate matter components in the United States. Environ Health Perspect 120(12):1699–1704

    Article  Google Scholar 

  • Berrocal VJ, Gelfand AE, Holland DM (2010a) A bivariate space-time downscaler under space and time misalignment. Ann Appl Stat 4(4):1942–1975

    Article  MathSciNet  MATH  Google Scholar 

  • Berrocal VJ, Gelfand AE, Holland DM (2010b) A spatio-temporal downscaler for output from numerical models. J Agric Biol Environ Stat 15(2):176–197

    Article  MathSciNet  MATH  Google Scholar 

  • Berrocal VJ, Gelfand AE, Holland DM (2012) Space-time data fusion under error in computer model output: an application to modeling air quality. Biometrics 68(3):837–848

    Article  MathSciNet  MATH  Google Scholar 

  • Bignal KL, Ashmore MR, Headley AD (2008) Effects of air pollution from road transport on growth and physiology of six transplanted bryophyte species. Environ Pollut 156(2):332–340

    Article  Google Scholar 

  • Billings P, Nolen JE, Tran T, Jump Z, Rappaport S, Edelman N, Rizzo A (2016) State of the air 2016. American Lung Association, Chicago

    Google Scholar 

  • Ceriani L, Verme P (2012) The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini. J Econ Inequal 10(3):421–443

    Article  Google Scholar 

  • Cisneros R, Brown P, Cameron L, Gaab E, Gonzalez M, Ramondt S, Veloz D, Song A, Schweizer D (2017) Understanding public views about air quality and air pollution sources in the San Joaquin Valley, California. J Environ Public Health 2017:1–7

    Article  Google Scholar 

  • De Oliveira V, Ecker MD (2019) A non-stationary non-Gaussian hedonic spatial model for house selling prices. Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2019.1704418

  • Draxler RR, Hess G (1998) An overview of the HYSPLIT\(\_4\) modelling system for trajectories. Aust Meteorol Mag 47(4):295–308

    Google Scholar 

  • Ecker MD, De Oliveira V (2008) Bayesian spatial modeling of housing prices subject to a localized externality. Commun Stat Theory Methods 37(13):2066–2078

    Article  MathSciNet  MATH  Google Scholar 

  • Ecker MD, De Oliveira V, Isakson H (2013) A note on a non-stationary point source spatial model. Environ Ecol Stat 20(1):59–67

    Article  MathSciNet  Google Scholar 

  • Escamilla V, Chibwesha CJ, Gartland M, Chintu N, Mubiana-Mbewe M, Musokotwane K, Musonda P, Miller WC, Stringer JS, Chi BH (2015) Distance from household to clinic and its association with the uptake of prevention of mother-to-child HIV transmission regimens in rural Zambia. J Acquir Immune Defic Syndr 70(3):e94–e101

    Article  Google Scholar 

  • Fecht D, Hansell AL, Morley D, Dajnak D, Vienneau D, Beevers S, Toledano MB, Kelly FJ, Anderson HR, Gulliver J (2016) Spatial and temporal associations of road traffic noise and air pollution in London: implications for epidemiological studies. Environ Int 88:235–242

    Article  Google Scholar 

  • Finley AO, Banerjee S, Gelfand AE (2015) spBayes for large univariate and multivariate point-referenced spatio-temporal data models. J Stat Softw 63(13):1–28

    Article  Google Scholar 

  • Fractracker Alliance (2021) Colorado oil & gas data. https://www.fractracker.org/map/us/colorado/

  • Friedman JM, Hagander L, Hughes CD, Nash KA, Linden AF, Blossom J, Meara JG (2013) Distance to hospital and utilization of surgical services in Haiti: do children, delivering mothers, and patients with emergent surgical conditions experience greater geographical barriers to surgical care? Int J Health Plan Manag 28(3):248–256

    Article  Google Scholar 

  • Geweke J (1991) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, vol 196. Federal Reserve Bank of Minneapolis, Research Department Minneapolis, Minneapolis

    Google Scholar 

  • González C, Gómez C, Rojas N, Acevedo H, Aristizábal B (2017) Relative impact of on-road vehicular and point-source industrial emissions of air pollutants in a medium-sized Andean city. Atmos Environ 152:279–289

    Article  Google Scholar 

  • Gray SC, Edwards SE, Miranda ML (2013) Race, socioeconomic status, and air pollution exposure in North Carolina. Environ Res 126:152–158

    Article  Google Scholar 

  • Henneman LR, Dedoussi IC, Casey JA, Choirat C, Barrett SR, Zigler CM (2020) Comparisons of simple and complex methods for quantifying exposure to individual point source air pollution emissions. J Exposure Sci Environ Epidemiol 31(4):654–663. https://doi.org/10.1038/s41370-020-0219-1

  • Hollister J, Shah T (2017) elevatr: access elevation data from various APIs. R package version 0.1.3. https://doi.org/10.5281/zenodo.400259

  • Huang C, Zhang H, Robeson SM (2011) On the validity of commonly used covariance and variogram functions on the sphere. Math Geosci 43(6):721–733

    Article  MathSciNet  MATH  Google Scholar 

  • Hughes-Oliver JM, Gonzalez-Farias G, Lu J-C, Chen D (1998) Parametric nonstationary correlation models. Stat Probab Lett 40(3):267–278

    Article  MATH  Google Scholar 

  • Hughes-Oliver JM, Heo T-Y, Ghosh SK (2009) An autoregressive point source model for spatial processes. Environmetr Off J Int Environmetr Soc 20(5):575–594

    MathSciNet  Google Scholar 

  • Hui EC, Liang C (2016) Spatial spillover effect of urban landscape views on property price. Appl Geogr 72:26–35

    Article  Google Scholar 

  • Kennedy M, Kopp S (2000) Understanding map projections. Environmental Systems Research Institute, Inc., Redlands

    Google Scholar 

  • Kim Y, Chun Y (2019) Revisiting environmental inequity in Southern California: does environmental risk increase in ethnically homogeneous or mixed communities? Urban Stud 56(9):1748–1767

    Article  Google Scholar 

  • Kim C, Daniels MJ, Hogan JW, Choirat C, Zigler CM (2019) Bayesian methods for multiple mediators: relating principal stratification and causal mediation in the analysis of power plant emission controls. Ann Appl Stat 13(3):1927–1956

    Article  MathSciNet  MATH  Google Scholar 

  • Kwak MY, Lee SM, Kim HJ, Eun SJ, Jang WM, Jung H, Kim Y, Lee JY (2019) How far is too far? A nationwide cross-sectional study for establishing optimal hospital access time for Korean pregnant women. BMJ Open 9(9):e031882

    Article  Google Scholar 

  • Mahalingaiah S, Hart JE, Laden F, Terry KL, Boynton-Jarrett R, Aschengrau A, Missmer SA (2014) Adult air pollution exposure and risk of uterine leiomyoma in the nurses’ health study II. Epidemiology 25(5):682–688

  • Martin R, Di Battista T, Ippoliti L, Nissi E (2006) A model for estimating point sources in spatial data. Stat Methodol 3(4):431–443

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen MA, Wiberg K, Ribeli E, Josefsson S, Futter M, Gustavsson J, Ahrens L (2017) Spatial distribution and source tracing of per-and polyfluoroalkyl substances (PFASs) in surface water in Northern Europe. Environ Pollut 220:1438–1446

    Article  Google Scholar 

  • Pan L, Yao E, Yang Y (2016) Impact analysis of traffic-related air pollution based on real-time traffic and basic meteorological information. J Environ Manag 183:510–520

    Article  Google Scholar 

  • Puett RC, Hart JE, Yanosky JD, Spiegelman D, Wang M, Fisher JA, Hong B, Laden F (2014) Particulate matter air pollution exposure, distance to road, and incident lung cancer in the nurses’ health study cohort. Environ Health Perspect 122(9):926–932

  • R Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Reich BJ, Yang S, Guan Y, Giffin AB, Miller MJ, Rappold AG (2020) A review of spatial causal inference methods for environmental and epidemiological applications. arXiv preprint arXiv:2007.02714

  • Rosofsky A, Levy JI, Zanobetti A, Janulewicz P, Fabian MP (2018) Temporal trends in air pollution exposure inequality in Massachusetts. Environ Res 161:76–86

    Article  Google Scholar 

  • Soriano MA Jr, Siegel HG, Gutchess KM, Clark CJ, Li Y, Xiong B, Plata DL, Deziel NC, Saiers JE (2020) Evaluating domestic well vulnerability to contamination from unconventional oil and gas development sites. Water Resour Res 56(10):e2020WR028005

    Article  Google Scholar 

  • Stein A, Draxler RR, Rolph GD, Stunder BJ, Cohen M, Ngan F (2015) NOAA’s HYSPLIT atmospheric transport and dispersion modeling system. Bull Am Meteorol Soc 96(12):2059–2077

  • United States Environmental Protection Agency (2021) EPA activities for cleaner air. https://www.epa.gov/sanjoaquinvalley/epa-activities-cleaner-air

  • Warren JL (2020) A nonstationary spatial covariance model for processes driven by point sources. J Agric Biol Environ Stat 25(3):415–430

    Article  MathSciNet  MATH  Google Scholar 

  • Warren JL, Grandjean L, Moore DA, Lithgow A, Coronel J, Sheen P, Zelner JL, Andrews JR, Cohen T (2018) Investigating spillover of multidrug-resistant tuberculosis from a prison: a spatial and molecular epidemiological analysis. BMC Med 16(1):122

    Article  Google Scholar 

  • Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 11(116):3571–3594

    MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Biostatistics, Yale University, New Haven, CT, 06510, USA

    Jiafang Song & Joshua L. Warren

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  1. Jiafang Song
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  2. Joshua L. Warren
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Correspondence to Joshua L. Warren.

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Song, J., Warren, J.L. A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source. JABES 27, 46–62 (2022). https://doi.org/10.1007/s13253-021-00466-y

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  • DOI: https://doi.org/10.1007/s13253-021-00466-y

Keywords

  • Bayesian modeling
  • Environmental inequity
  • Gaussian process
  • Spatial analysis